Related papers: Cartesian products of two $CR$ sets

It is known that the spatial product of two product systems is intrinsic. Here we extend this result by analyzing subsystems of the tensor product of product systems. A relation with cluster systems is established. In a special case, we…

In this paper, we give a combinatorial proof of a positivity result of Chern related to Andrews's $\mathcal{EO}^*$-type partitions. This combinatorial proof comes after reframing Chern's result in terms of copartitions. Using this new…

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…

We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…

We give an elementary proof of low rank cases of the conjecture that the tensor product of two semistable Euclidean lattices is again semistable.

Given two associative algebras A, C and a linear space V together with some linear maps R_1, R_2, R_3, E satisfying some conditions, we define an associative algebra structure on A\otimes V\otimes C called a two-sided crossed product.…

The Central Sets Theorem, a fundamental result in Ramsey theory, is a joint extension of both Hindman's theorem and van der Waerden's theorem. It was originally introduced by H. Furstenberg using methods from topological dynamics. Later,…

We define graph products of families of pairs of groups and study the question when two such graph products are commensurable. As an application we prove linearity of certain graph products.

We show that the intersection of the rational derived series of a one-relator group is rationally perfect and is normally generated by a single element. As a corollary, we characterise precisely when a one-relator group is residually…

In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

Kang et al. provided a path realization of the crystal graph of a highest weight module over a quantum affine algebra, as certain semi-infinite tensor products of a single perfect crystal. In this paper, this result is generalized to give a…

In this note we extend duality theorems for crossed products obtained by M. Koppinen and C. Chen from the case of a base field or a Dedekind domain to the case of an arbitrary noetherian commutative ground ring under fairly weak conditions.…

Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.

We construct a set of strong recurrence which is not a van der Corput set. This shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurrence. In addition, we derive that the class of sets of strong…

Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundamental properties and isolate some new ones, including a…

All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.

The category of crossed complexes gives an algebraic model of the category of $CW$-complexes and cellular maps. We explain basic results on crossed complexes which allow the computation of free crossed resolutions of graph products of…

We prove several results on products of conjugacy classes in finite simple groups. The first result is that there always exists a uniform generating triple. This result and other ideas are used to solve a 1966 conjecture of Peter Neumann…

Inspired by the definition of generalized wreath product of permutation groups, we define the generalized wreath product of graphs, containing the classical Cartesian and wreath product of graphs as particular cases. We prove that the…